Conventionally, a resin film material (such as a film and a sheet) has been widely used as a material of a separator for use in a battery. The resin film material, of which a separator original sheet is made up, is produced by being stretched in a width direction (transverse direction). This causes the resin film material to be a porous film material in which fine pores are formed in submicron order. The separator original sheet, which is made up of such a porous film material, is slit, by a slitting apparatus, into a plurality of separators each having a desired width (Patent Literature 1).